The double headed eagle is a symbol of Freemasonry in general. But this headgear comes from the Scottish Right --one of Freemasonry's appendant organizations. The 32 inside of the red triangle refers to the 32nd degree of Scottish Right Freemasonry. This is the highest level of the Scottish Right. (33 exists only as an honorific degree, awarded to members who do exceptional things.)

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Originally Posted by J Darnielle

Bought this at an estate thinking it was a Shriner's hat. It is not.
Thanks!

Double headed eagle is a symbol of the Byzantine Empire and former constituents. In Eastern Christian interpretations means an eagle facing Rome (West) and Constantinople (East). Three modern day countries that still carry the double headed eagle on their flags include Russia, Serbia and Albania.